journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Research Paper
Fatigue surviving, fracture resistance, shear stress and finite element analysis of glass fiber posts with different diameters Vinı´cius Felipe Wandschera, Ce´sar Dalmolin Bergolib, Ariele Freitas de Oliveirac, Osvaldo Bazzan Kaizera, Alexandre Luiz Souto Borgesd, Ina´cio da Fontoura Limberguere, Luiz Felipe Valandroa,n a
Graduate Program in Oral Science (Prosthodontic Unit), Faculty of Odontology, Federal University of Santa Maria, Santa Maria, Brazil b Division of Prosthodontics, Department of Restorative Dentistry, Federal University of Pelotas, Rio Grande do Sul, Brazil c Faculty of Odontology, Federal University of Santa Maria, Santa Maria, Brazil d Institute of Science and Technology, Univ Est Paulista Julio de Mesquita Filho, São José dos Campos, SP, Brazil e Faculty of Mechanical Engineering, Federal University of Santa Maria, Santa Maria, Brazil
art i cle i nfo
ab st rac t
Article history:
This study evaluated the shear stress presented in glass fiber posts with parallel fiber (01)
Received 26 September 2014
and different coronal diameters under fatigue, fracture resistance and FEA. 160 glass-fiber
Received in revised form
posts (N¼ 160) with eight different coronal diameters were used (DT ¼double tapered,
14 November 2014
number of the post¼ coronal diameter and W¼Wider - fiber post with coronal diameter
Accepted 17 November 2014
wider than the conventional): DT1.4; DT1.8 W; DT1.6; DT2W; DT1.8; DT2.2 W; DT2; DT2.2.
Available online 11 December 2014
Eighty posts were submitted to mechanical cycling (3 106 cycles; inclination: 451; load:
Keywords:
50 N; frequency: 4 Hz; temperature: 37 1C) to assess the surviving under intermittent
Fiber post
loading and other eighty posts were submitted to fracture resistance testing (resistance
Fracture strength
[N] and shear-stress [MPa] values were obtained). The eight posts types were 3D modeled
Mechanical cycling
(Rhinoceros 4.0) and the shear-stress (MPa) evaluated using FEA (Ansys 13.0). One-way
Finite element analysis
ANOVA showed statistically differences to fracture resistance (DT2.2 W and DT2.2 showed
Fractographic analysis
higher values) and shear stress values (DT1.4 showed lower values). Only the DT1.4 fiber posts failed after mechanical cycling. FEA showed similar values of shear stress between the groups and these values were similar to those obtained by shear stress testing. The failure analysis showed that 95% of specimens failed by shear. Posts with parallel fiber (01) may suffer fractures when an oblique shear load is applied on the structure; except the thinner group, greater coronal diameters promoted the same shear stresses. & 2014 Elsevier Ltd. All rights reserved.
n
Corresponding author. Tel.: þ55 55 3220 9276; fax: þ55 55 3220 9272. E-mail addresses: [email protected] (V.F. Wandscher), [email protected] (C.D. Bergoli), [email protected] (A.F. de Oliveira), [email protected] (O.B. Kaizer), [email protected] (A.L. Souto Borges), [email protected] (I.d.F. Limberguer), [email protected] (L.F. Valandro). http://dx.doi.org/10.1016/j.jmbbm.2014.11.016 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
70
1.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Introduction
Researchers have recently studied alternatives for improving the resistance of endodonticaly treated teeth. The amount of remaining coronal structure is used to determine if the use of fiber reinforced posts is necessary to retain the restoration material (Ferrari and Scotti, 2002). Teeth restored with prefabricated metallic posts or cast posts and cores have shown high values of fracture resistance (Silva et al., 2010; Silva et al., 2011). However, the mode of failure for these teeth is unfavorable, causing irreversible fractures and loss of the teeth. This mode of failure can be explained due the elastic modulus of these posts; with metallic posts presenting greater elastic moduli than fiber posts and generating elevated stress concentration on the remaining root structure (Silva et al., 2011; Akkayan and Gülmez, 2002; Ferrari et al., 2000, 2007; Giovani et al., 2009; Hayashi et al., 2006; Li et al., 2011; Padmanabhan, 2010). The elastic modulus is representative of the flexibility of a material, where higher values indicate a hard material and lower values indicating a flexible material (Plotino et al., 2007). The diameter, the type of fiber and the resin material can influence the elastic limit of a pre-fabricated fiber reinforced post (Asmussen et al., 1999). The elastic modulus is related to the stress transmitted to the root, being one of the most important factors in the fracture mechanism (Coelho et al., 2009; Spazzin et al., 2009; Pegoretti et al., 2002). In vitro (Akkayan and Gülmez, 2002; Coelho et al., 2009; Spazzin et al., 2009; Pegoretti et al., 2002) and clinical studies (Ferrari et al., 2000; Ferrari et al., 2007; Schmitter et al., 2007) have shown better or at least comparable performance for fiber reinforced composite posts when compared with cast post and cores and pre-fabricated metallic posts (reparable failures for fiber post approach, while irreparable fractures occur for metal post). Thus, adhesively cemented fiber posts have been indicated as a better option to restore endodonticaly treated teeth, especially in terms of minimal intervention and reducing the risk of root fracture (Ferrari and Scotti, 2002; Ferrari et al., 2000; Ferrari et al., 2007; Malferrari et al., 2003; Monticelli et al., 2003). Static tests are important for assessing the maximum load required for rupture of a specimen. Most articles use the fracture resistance test (loaded at 451) to assess the behavior of fiber posts (Silva et al., 2010, 2011; Akkayan and Gülmez, 2002; Asmussen et al., 1999). However, parallel fiber (01) reinforced polymers usually fracture due to shear stress when submitted at oblique forces. Glass fiber posts are classified as a fiber reinforced polymeric material; where fiber arrangement is crucial in understanding their failure mode. The fiber posts usually present longitudinally organized fibers (parallel 01), which can support high tensile stresses. On the other hand, the shear stresses destructively affect the polymer, indicating that the polymer matrix is important in the calculation of these fracture values (Shipley and Becker, 2002). FEA is a numerical method that help to investigate stress and strain state and combined with experimental test allows obtaining a better understanding of failures, predicting where failure can occur. Hence, the use of both tests is important to obtain a better understanding regarding the mechanical
behavior of a specimen during an event (Farah et al., 1973; Soares et al., 2008; Versluis et al., 2006). Although there are studies showing that fiber reinforced post have good properties, there are some concerns regarding their use to restore weakened roots. Therefore, some techniques have been developed to guarantee better results when restoring weakened roots (anatomic post, accessory fiber post, glass fiber strips, composite resin) (Bonfante et al., 2007; Martelli et al., 2008; Gonçalves et al., 2006; Grandini et al., 2003; Island and White, 2005; Marchi et al., 2003; Miller, 1993). These techniques lead to decreasing the amount of resin cement around the fiber post and provide good fracture resistance to the weakened root. However, these techniques are not easy to perform and require more clinical time when compared to the use of conventional fiber post cementation. Some tapered fiber posts present enlarged coronal/cervical diameters for restoring weakened roots by not requiring excess removal of the intracanal dental structure. Thus, these posts maintain a conservative dimension of the apical portion of a root canal and decrease the resin cement thickness around the post at the weakened portion of the root. These wider posts have a greater taper when compared with conventional posts; however, these posts keep the same fiber/matrix (80/20) ratio. However, there are no studies regarding the fracture resistance or the behavior of this type of post system during mechanical loading. Consequently, this current study aimed to evaluate the fracture resistance, shear stress (in vitro and FEA test) and surviving after intermittent fatigue loading of fiber posts with different coronal wider diameters. The following conceptual hypotheses were tested: (1) fiber posts with increased coronal diameters would present higher rates of fracture resistance; (2) the finite element analysis would show similiar distribution for all groups without difference between real and virtual shear values calculated; (3) fiber posts with increased coronal diameters would present the best behavior during mechanical cycling.
2.
Material and methods
2.1.
Specimen preparation and embedding procedures
The posts used in the study are part of a system of fiberreinforced polymers with double tapered (DT) shape. In this set of posts there are special retainers for larger root canals in which the coronary diameters are wider, but the apical is smaller relative to the other. So the groups was named according to factors: DT (double-tapered)þcoronal diameter (for the wider posts the W letter was added in the name). One hundred sixty fiber posts (White Post DC and White Post DCE systems, FGM, Joinvile, SC, Brazil) (N¼ 160) were allocated into eight groups (n¼20) (Fig. 1A). Each post was attached to a device, keeping its long axis perpendicular to the ground, and embedded with epoxy resin (Sikadur 55 SLV, Osasco, SP, Brazil) in plastic cylinders (height: 15 mm, Ø: 25 mm). The fiber posts from the conventional system (White Post DC) were embedded to a depth of 14 mm, while the wider fiber posts of the special system (White Post DCE) were embedded to a depth of 12 mm. This difference in embedding length was
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
71
Fig. 1 – A. Representative image of the study groups utilized (DT¼ Double tapered and the number, for example, 1.4, indicate the coronal diameter). White letters indicates the group's code, the red upper numbers indicates the coronal diameter and the red lower numbers the apical diameters. B. Specimen positioned during mechanical cycling.
Fig. 2 – Mathematical deduction to calculate the shear stress. τ: shear stress, V: applied force (Fy: Fmax * cos451), Q: static – : center of gravity refers to a semi-circle). The area to be calculated should be taken moment of area (A: area under the circle* y by half as demonstrated in Fig. 6 (SHEAR stress graphic), I: inertia moment of circle area, t: thickness of cross-sectional area (post diameter), π: 3.14 and D: post diameter.
necessary to keep the same length of the fiber posts to the coronal portion (cylindrical region, 6 mm), since conventional posts are 20 mm in length and wider special posts are 18 mm in length. So it was possible to ensure full embedding of tapered region and assure that the load be distributed throughout the cylindrical length of the fiber post.
2.2.
Evaluation of surviving after mechanical cycling
Ten specimens of each group were submitted to mechanical cycling, in a mechanical fatigue simulator (Erios ER 1 force of 11000, Erios, São Paulo, SP, Brazil), applying the protocol as followed: angle- 451; load- 50 N; frequency- 4 Hz; temperature- 737 1C. During the cycling, a cylindrical stainless steel piston (Ø: 6 mm) applied a load to the coronal portion of the post to a maximum of 3,000,000 cycles or until fracture (Fig. 2). Specimens were analyzed after every interval of 250,000 cycles.
2.3.
Fracture resistance test
A stainless steel piston with a diameter of 6 mm, attached to a universal testing machine (EMIC DL 2000, São José dos Pinhais, PR, Brazil), applied a force on the coronal portion of the specimens (Fig. 1B), at a cross head speed of 1 mm/min, 451 of inclination until fracture. The value of fracture resistance (N) of each specimen was defined as the highest point observed in the load x dislodgement curve. After the fracture resistance test, the shear stress value (MPa) of each specimen was calculated. To calculate the shear stress of the cross-section circular area of the fiber post, it was necessary to determine the formula from a universal formula for the shear stress (Fig. 2). Then, the calculation was performed according to the following mathematical equation: τ¼
16:Fmax:cos45 3:π:D2
ð1Þ
where, τ¼shear stress; Fmax.cos45¼refers to vector component Fy, responsible for specimen bending (Fig. 3), Fmax¼ maximum
72
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Fig. 3 – A: Specimen positioned during the fracture resistance test and the vectorial force decomposition (original force at 451). B: Parallelogram Law for calculating force vectors (Hibbeler, 2006; Beer and Johnston, 1994), F: Original Force at 451, HIP: hypotenuse, Fy: vectorial component at Y axis, OS: opposite side to the angle, Fx: vectorial component at X axis and AS: adjacent side to the angle. So, HIP¼F, Fy¼OS and Fx¼AS.
value (N) observed at specimen fracture, cos45¼ cosine of the angle 451; D¼diameter of the post at the coronal portion (mm). Values of “stress” were obtained for each specimen and a mean was calculated for each group.
2.4.
Failure analysis
After evaluating the fracture resistance, all specimens were analyzed using a stereomicroscope at 10x (Discovery V-20, Zeiss, Germany) to detect the type of failure. Some specimens were observed with a scanning electron microscope (SEM) (JSM 5400, Jeol Ltd, Tokyo, Japan).
2.5.
Finite element analysis
The specimens corresponding to the conventional fiber post system (White Post DC, FGM) and wider fiber post system (White Post DCE, FGM) were 3D modeled using the software CAD Rhinoceros (version 4.0SR8 McNell, North America, Seattle, WA, USA) in accordance with the dimensions obtained from the manufacturer (Fig. 1). The epoxy resin was modeled in accordance with the plastic cylinder dimensions (15 mm height and 25 mm diameter). After modeling, the geometries were imported in an.STP format to the Ansys software (Ansys 13.0, Houston, TX, USA) for numerical simulation. Tetrahedron elements were used to generate the mesh using 10 nodes, with a size of 0.2mm, totaling approximately 80,000 elements and 120,000 nodes in each model. The interface between the fiber post and epoxy resin was considered bonded, the lateral and inferior surfaces of the epoxy resin were considered fixed (no displacement) and a force at 45o of angulation was applied to the fiber post. The force applied in each model was the same as the fracture resistance mean obtained in each group after fracture resistance test (Table 1), so the force applied to each group were: DT1.4 - 66 N; DT1.8 W - 144 N, DT 1.6–110 N; DT2W – 170 N; DT1.8–132 N; DT2.2 W – 237 N; DT2–169 N; DT2.2 196 N. The shear stress values (MPa)
were analyzed in each group at a point situated 2 mm above the fulcrum region. In bending the shear stress it is maximum and constant in the average central plan (center) of the post in all extension (6mm), differently the tensile and compressive stresses (Shipley and Becker, 2002). Fiber posts were considered orthotropic (Ex ¼ 37 GPa; Ey ¼9.5 GPa; Ez ¼ 9.5 GPa; vxy ¼0.27; vxz ¼ 0.34; vyz ¼ 0.27; Gxy ¼ 3.1; Gxz ¼ 3.5; Gyz ¼ 3.1) and the epoxy resin was considered isotropic (E¼2.2 GPa; v¼ 0.3). Orthotropic materials present Young modulus values in accordance with the axis (x, y, z), while isotropic materials presented just one value of Young modulus. The elastic and poison values used for fiber post were in accordance with the literature (Lanza et al., 2005), while the values of epoxy resin were obtained from the manufacture (Sikadur, Osasco, SP, Brazil). These values were inserted in the software before execute the analysis.
2.6.
Statistical analysis
The mean values of fracture resistance and shear stress were submitted to One-way ANOVA and Tukey test (α¼0.05). The specimens submitted to mechanical cycling were analyzed in accordance with two conditions: fracture and no fracture.
3.
Results
3.1.
Fracture load and stress analysis
All specimens of DT1.4 fractured during mechanical cycling: five specimens failed between 0 and 250,000 cycles; two specimens failed between 250,000 and 500,000 cycles; two specimens failed between 500,000 and 750,000 cycles; and one specimen failed between 750,000 and 1,000,000 cycles. Other groups did not present failures. One way ANOVA showed a statistically significant difference between the groups, in relation to the fracture strength (po0.001) and shear stress values (po0.001). Fiber posts with smaller coronal diameters showed lower fracture resistance values (N) (Table 1) when compared with fiber posts with wider coronal diameters. However, these fiber posts supported almost the same stress values (MPa) during the test. The fiber posts of the DT1.4 group showed statistically significantly lower shear stress values than did the other groups (Table 1). The graphics load (N) X displacement (mm) cans be observed in Fig. 4. The finite element analysis showed that the shear stress (MPa) achieved higher values at the centrum of the fiber posts and minimal values at the peripheral regions (Fig. 5). The values and the distribution of shear stresses were similar in all groups and similar to the values obtained by the shear stress calculation.
3.2.
Failure analysis
The fracture analysis showed that 95% of the specimens presented a crack along the long axis, perpendicular to the applied direction of the load (Fig. 6ABC). Another 5% of specimens the failure standard was practically in cracks with “Y” appearance (Fig. 6D), with two crack starting at the point
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
73
Table 1 – Means and standard deviation to the values of fracture resistance (N) and shear stress (MPa) after Tukey tests (α ¼0.05). Posts
Coronal Ø (mm)
Mean fracture resistance and standard deviation (N)
Mean shear stress (MPa) and standard deviation
DT1.4 DT1.8W DT1.6 DT2W DT1.8 DT2.2W DT2 DT2.2
1.4 1.8 1.6 2.0 1.8 2.2 2.0 2.2
66.679.01A 140.8977.59B 110.83711.76C 172.91713.82D 132.07711.79B 217.35718.73E 169.27724.66D 196.76712.06E
40.4275.47a 51.7072.78b 51.4875.46b 51.3974.10b 48.4774.32b 53.3974.60b 50.3177.33b 48.3472.96b
* Same letters mean similar statistical results.
Fig. 4 – Representatives images of load (N) X Displacement (mm) graphics of eight groups submitted at fracture resistance. CP: each curve in each graph represents a specimen. of load application that join the center of the specimen ending at the external portion of the post. The fracture analysis with the Scanning Electron Microscope (SEM) presented a characteristic fracture pattern of shear stresses, a crack in the central portion along the long axis of the posts (Fig. 6ABC) in the same sense of the fibers of the posts (parallel fibers).
4.
Discussion
In accordance with Asmussen et al. Asmussen et al. (1999), the highest value of resistance of a post could be obtained using the force X deformation plot. This property is related to the force necessary to cause a fracture or plastic deformation in a material (Anusavice, 2003), leading to catastrophic failure of a specimen (Fig. 4). The results of this current study showed that the fracture resistance values increase as the diameter of the fiber post increases (Table 1), corroborating with the results of Asmussen et al. Asmussen et al. (1999) and confirming the first hypothesis of the study. This result is explained by the fiber posts with smaller diameters (DT1.4) fractured with lower values comparing to another groups with wider diameters Asmussen et al. (1999). A fiber post is composed of longitudinal fibers embedded in an epoxy resin matrix, which is prone to failure due to shear stresses. The parallel configuration of fibers (01) in fiber
posts is very resistant to tensile forces applied along the long axis of the posts. However, when a force is obliquely applied, this resistance can be affected because other types of stresses start acting on this polymer (such as shear stress). Hence, the integrity of the material is impaired, since these posts were not designed to withstand oblique loads. Fracture occurs more easily by shear stress, and occurs at lower numerical values than the tensile stresses that the material supports. Thus, it is also important to perform failure analysis and calculate the shear stress to evaluate this kind of post. Based on the shear stress results, the second hypothesis was partially accepted, since the shear stress obtained by the fiber post DT1.4 was statistically lower than the other groups (Table 1). Normally, the shear stress should be identical for all groups, because the posts are made with the same material and proportions (80% glass fibers and 20% epoxy resin matrix). However, the DT1.4 fiber posts present the smallest coronal diameter (ؼ1.4 mm), which is directly proportional to the shear stress values and generates results that are statistically inferior. In addition, this result corroborates with the failures observed by this type of fiber post after mechanical cycling (all specimens failed), indicating that the DT1.4 fiber post system (Øc¼ 1.4 mm and Øa¼ 0.65 mm) is the most susceptible to shear stress forces than the other groups. The finite element analysis showed a similar distribution of shear stress between the groups, accepting partially the second hypothesis of the study. Additionally, the values of
74
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Fig. 5 – Representatives images of the finite element analysis of each model. In each group was chosen a point for measuring the stress (2 mm above the fulcrum). It is important to observe that the maximum shear stress occur in the central portion of the posts (points A2, B2, C2, D2, E2, F2, G2 and H2) and the minimum shear stress occur in the external portion of the posts. The maximum shear stress values are similar to those obtained by the shear stress calculation (Table 1).
Fig. 6 – Representative image of failure analysis in stereomicroscope (X10). In A, B and C are represent the failures of the 95% of specimens. A and C lateral views and B top view. The red arrow indicates the point of load application and the manual indicator show the cracks. It notes a crack in the long axis and approximately in center of specimen consequence of the shear stress produced during fracture load. In D is the different failure pattern (another 5% of specimens).
Fig. 7 – Representatives micrographics of central portion of posts. To analyze these surfaces has required a cut in the area of the fulcrum. After this cut the portions were detached and observed in SEM. The letters a indicate the fibers, b the matrix, c show the hackles areas (concavities) and d indicate the scallops. As c as d affect the resin matrix. The red arrows indicate the loading direction. Perceives in both A and B, zones shear rupture characteristics, presenting hackles and scallops (“undulations”) in resin portion (matrix) of posts.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
shear stress observed by the finite element analysis (Fig. 5) were similar to those obtained by the formula calculation (Table 1), in all groups. These results prove that the shear stresses are harmful to fiber posts, validating these results and confirming the mechanical behavior of this kind of post. The failure analysis indicated that fiber posts fail by shear stress, since 95% of the specimens showed typical shear stress failure patterns (Figs. 6 and 7). Another 5% of failures present a pattern as in image 5D breaking by shear stress too. This pattern can be explained by small misalignment of the specimen during the embedding. How the test is performed in small areas, a small error in aligning the specimen may to generate this failure pattern, but that does not affect the stress and fracture values. In order to understand the failures, it is necessary to understand the 451 loading on the specimens. As indicated by the parallelogram law, a 451 force must be decomposed into a cartesian axis (Hibbeler, 2006). The combined vector components of X and Y give rise to the original force F at 451 (Fig. 3). The component X causes compressive stresses to the structure (Fig. 8A) while the Y component leads to bending of the post and the appearance of tensile, compression (Fig. 8B) and shear stresses (Fig. 8C). The tensile and compression stresses are maximum in the external portions and minimum at the center (neutral line) (Fig. 8B). The opposite occurred with the shear stress, where the maximum force occurred in the center and minimum forces were at the external surfaces of the posts (Fig. 8C) (Beer and Johnston, 1994). As the shear stress is greatest at the center of the specimen, the fracture tends to occur in this zone, inducing fracture of the structure as presented in Fig. 6. Thus, during bending, the limit of shear resistance is reached before the limit of tensile resistance is attained, because the fiber posts were not designed to support shear stress. The finite element analysis (Fig. 5) and the failure mode evaluation (Fig. 6) support these findings. Fractures in composites can occur in a number of complex ways, due to their laminated orthotropic construction
Fig. 8 – ABC. Representation of the Fx and Fy effects on the structure. C (graphic B): compression, T: tensile, NL: neutral line, σx: normal tension in X axis, A: area, M: static moment of area, C (formula): distance from neutral line to the more requested fiber, I: inertia moment of the area,τ: shear stress, V: applied force (Fy¼ Fmax * cos451), Q: static moment of area (A: circular area) and t: thickness of cross-sectional area (post diameter).
75
(the fracture depends on the direction of applied load and the orientation of fibers). Fractures in continuous fiber reinforced composites can be divided into three basic fracture types: interlaminar (fractures oriented between plies), intralaminar (fractures located internally within a ply) and translaminar (involving significant fiber fractures). For these cases, interlaminar and intralaminar fractures occur on a plane that is parallel to that of fiber reinforcement. The interlaminar and intralaminar fractures occur under mode I tension (generated under interlaminar tension), mode II in-plane shear (separation under shear loading occurs by coalescence of numerous tensile microcracks under continued shear displacement) and mode III anti-plane shear (which have not been thoroughly studied) (Shipley and Becker, 2002). As inter- and intralaminar fractures occur in the same plane as their fiber reinforcement, their fracture mechanism and appearance tend to be dominated by fracture of the matrix and fiber-to-matrix separation. In addition, Fig. 7 presents a distinct branched structure that exists on both sides of the hackles and scallops, where they intersect adjoining areas of fiber-to-matrix separation (Shipley and Becker, 2002). These failures are classified as intralaminar mode II in-plane shear. Several fiber posts (fiber-reinforced polymer) are commercially available. Most of them, such fibers are arranged in parallel along the post. Thus, in situations where an anterior tooth (451 of inclination) should be restored, it is very important to understand how these forces act on these teeth, especially on bending (tensile, compression and shear stresses). The arrangement of the fibers plays great importance when a force is applied to this structure. Fiber posts with parallel fibers efficiently support tensile, but in bending these fibers are not as efficient. This leads to the failure by shear. In teeth restored with fiber posts, a core is made with composite resin. This causes an increase in resistance, but it does not prevent the bending movement of the restorative assembly. In addition to the in vitro tests, dynamic tests, such as fatigue, are important for predicting the material behavior. Mechanical cycling has been used for testing the bond between fiber posts and root canals (Bergoli et al., 2011; Bottino et al., 2007; Rosa et al., 2011; Valandro et al., 2009), the behavior of endodontically treated teeth restored with post retainers (Bolhuis et al., 2004; Santini et al., 2011; Reid et al., 2003) and for evaluating the properties of different restorative materials (Rached et al., 2011; Scherrer et al., 2011). Mechanical cycling is an important test because it can generate a catastrophic failure from defects inside the material, after long periods of cycling (Wiskott et al., 1995), which is similar to what occurs clinically. As prospective studies, the researchers should investigate if the findings/ outcomes with fiber posts observed by us will occur when restoring root canals with fiber post, core and crown. Based on the results obtained after mechanical cycling, the third hypothesis of the study was partially accepted, because even though all specimens of group DT1.4 fractured during mechanical cycling, the other groups did not present failures after three million cycles. This outcome could be related to the fact that the fracture resistance mean of fiber post DT1.4 (Øc¼ 1.4 and Øa¼ 0.65) was inferior to the load used during mechanical cycling, allowing the fiber post to
76
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
reach its elastic limit. Also, this study performed 3,000,000 cycles, corresponding to three years of clinical service (Wiskott et al., 1995). It has been proposed that, if more cycles had been applied, the other groups might have failed.
5.
Conclusion
1- Fiber posts with fibers arranged parallel to the long axis presented failures by shear stress forces when loading at 451. 2- The DT1.4 fiber post appears to be less resistant to fracture than the other posts. 3- The fracture resistance of a fiber post increases when increasing the coronal diameter. 4- Finite element analysis, in association with in vitro test, validates the hypothesis that fiber posts failure by shear stress when forces are loading at 451.
Acknowledgments The authors thank CAPES (Brazilian Higher Education Agency, Brazil) and CNPq (National Council for Scientific Development and Technology, Brazil) by supporting this investigation. They also thank FGM (Joinville, SC, Brazil) for material donation.
references
Akkayan, B., Gu¨lmez, T., 2002. Resistance to fracture of endodontically treated teeth restored with different post systems. J. Prosthet. Dent. 87, 431–437. Anusavice, K.J., 2003. Philips’ Science of Dental Materials, eleventh ed. Saunders Co., St. Louis. Asmussen, E., Peutzfeldt, A., Heitmann, T., 1999. Stiffness, elastic limit, and strength of newer types of endodontics posts. J. Dent. 27, 275–278. Beer, F.P., Johnston Jr., R., 1994. Vector Mechanics for Engineers Statics, fifth ed. Makron Books do Brasil. Bergoli, C., Amaral, M., Baldissara, P., Valandro, L.F., 2011. Surviving of bovine teeth adhesively restored with 3 types of fiber post after fatigue resistance. Minerva Stomatol. 60, 303–309. Bolhuis, P., Gee, A., Feilzer, A., 2004. Influence of fatigue loading on four post-and-core systems in maxillary premolars. Quintessence Int. 35, 657–667. Bonfante, G., Kaizer, O.B., Pegoraro, L.F., do Valle, A.L., 2007. Fracture strength of teeth with flared root canals restored with glass fibre posts. Int. Dent. J. 57, 153–160. Bottino, M.A., Baldissara, P., Valandro, L.F., Galhano, G.A., Scotti, R., 2007. Effects of mechanical cycling on the bonding of zirconia and fiber posts to human root dentin. J. Adhes. Dent. 9, 327–331. Coelho, C.S., Biffi, J.C., Silva, G.R., Abraha˜o, A., Campos, R.E., Soares, C.J., 2009. Finite element analysis of weakened roots restored with composite resin and posts. Dent. Mater. J. 28, 671–678. Farah, J.W., Craig, R.G., Sikarskie, D.L., 1973. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J. Biomech. 6, 511–520. Ferrari, M., Scotti, R., 2002. Fiber Posts. Theoretical Considerations and Clinical Applications, first ed. Milan, Masson39–41.
Ferrari, M., Vichi, A., Garcı´a-Godoy, F., 2000. Clinical evaluation of fiber-reinforced epoxy resin posts and cast post and cores. Am. J. Dent. 13, 15B–18B. Ferrari, M., Cagidiaco, M.C., Goracci, C., Vichi, A., Mason, P.N., Radovic, I., Tay, F., 2007. Long-term retrospective study of the clinical performance of fiber posts. Am. J. Dent. 20, 287–291. Giovani, A.R., Vansan, L.P., Sousa Neto, M.D., Paulino, S.M., 2009. In vitro fracture resistance of glass-fiber and cast metal posts with different lengths. J. Prosthet. Dent. 101, 183–188. Gonc¸alves, L.A., Vansan, L.P., Paulino, S.M., Sousa Neto, M.D., 2006. Fracture resistance of weakened roots restored with a transilluminating post and adhesive restorative materials. J. Prosthet. Dent. 96, 339–344. Grandini, S., Sapio, S., Simonetti, M., 2003. Use of anatomic post and core for reconstructing an endodontically treated tooth: a case report. J. Adhes. Dent. 5, 243–247. Hayashi, M., Takahashi, Y., Imazato, S., Ebisu, S., 2006. Fracture resistance of pulpless teeth restored with post-cores and crowns. Dent. Mater. 22, 477–485. Hibbeler, R.C., 2006. Mechanics of Materials, fifth ed. Prentice Hall, Sa˜o Paulo Pearson. Island, G., White, G.E., 2005. Polyethylene ribbon fibers: a new alternative for restoring badly destroyed primary incisors. J. Clin. Pediatr. Dent. 29, 151–156. Lanza, A., Aversa, R., Rengo, S., Apicella, D., Apicella, A., 2005. 3D FEA of cemented steel, glass and carbon posts in a maxillary incisor. Dent. Mater. 21, 709–715. Li, Q., Yan, P., Chen, Z., 2011. Fracture resistance and failure patterns of open apex root teeth with different posts after endodontic treatment. J. Huazhong. Univ. Sci. Technol. Med. Sci. 31, 271–276. Malferrari, S., Monaco, C., Scotti, R., 2003. Clinical evaluation of teeth restored with quartz fiber-reinforced epoxy resin posts. Int. J. Prosthodont. 16, 39–44. Marchi, G.M., Paulillo, L.A., Pimenta, L.A., Lima, F.A., 2003. Effect of different filling materials in combination with intraradicular posts on the resistance to fracture of weakened roots. J. Oral. Rehab. 30, 623–629. Martelli Jr., H., Pellizzer, E.P., Rosa, B.T., Lopes, M.B., Gonini Jr., A., 2008. Fracture resistance of structurally compromised root filled bovine teeth restored with accessory glass fibre posts. Int. Endod. J. 41, 685–692. Miller, T.E., 1993. A new material for periodontal splitting and orthodontic retention. Comp. Cont. Educ. Dent. 14, 802–804. Monticelli, F., Grandini, S., Goracci, C., Ferrari, M., 2003. Clinical behavior of translucent-fiber posts: a 2-year prospective study. Int. J. Prosthodont. 16, 593–596. Padmanabhan, P., 2010. A comparative evaluation of the fracture resistance of three different pre-fabricated posts in endodontically treated teeth: an in vitro study. J. Conserv. Dent. 13, 124–128. Pegoretti, A., Fambri, L., Zappini, G., Bianchetti, M., 2002. Finite element analysis of a glass fibre reinforced composite endodontic post. Biomaterials 23, 2667–2682. Plotino, G., Grande, N.M., Bedini, R., Pameijer, C.H., Somma, F., 2007. Flexural properties of endodontic posts and human root dentin. Dent. Mater. 23, 1129–1135. Rached, R.N., Souza, E.M., Dyer, S.R., Ferracane, J.L., 2011. Dynamic and static strength of an implant-supported overdenture model reinforced with metal and nonmetal strengtheners. J. Prosthet. Dent. 106, 297–304. Reid, L.C., Kazemi, R.B., Meiers, J.C., 2003. Effect of fatigue testing on core integrity and post microleakage of teeth restored with different post systems. J. Endod. 29, 125–131. Rosa, R.A., Bergoli, C.D., Kaizer, O.B., Valandro, L.F., 2011. Influence of cement thickness and mechanical cycling on the push-out bond strength between posts and root dentin. Gen. Dent. 59, 156–161.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Santini, M.F., Wandscher, V., Amaral, M., Baldissara, P., Valandro, L.F., 2011. Mechanical fatigue cycling on teeth restored with fiber posts: impact of coronal grooves and diameter of glass fiber post on fracture resistance. Minerva Stomatol. 60, 485–493. Scherrer, S.S., Cattani-Lorente, M., Vittecoq, E., de Mestral, F., Griggs, J.A., Wiskott, H.W., 2011. Fatigue behavior in water of Y-TZP zirconia ceramics after abrasion with 30 μm silicacoated alumina particles. Dent. Mater. 27, 28–42. Schmitter, M., Rammelsberg, P., Gabbert, O., Ohlmann, B., 2007. Influence of clinical baseline findings on the survival of 2 post systems: a randomized clinical trial. Int. J. Prosthodont. 20, 173–178. Shipley, R.J., Becker, W.T., 2002. Failure analysis continuous fiber reinforced composites. In: tenth ed. In: Smith, T.W., Grove, R.A. (Eds.), ASM Handbook: Failure Analysis and Prevention, volume 11. ASM International, Ohio, pp. 731–743. Silva, G.R., Santos-Filho, P.C., Simamoto-Ju´nior, P.C., Martins, L.R., Mota, A.S., Soares, C.J., 2011. Effect of post type and restorative techniques on the strain and fracture resistance of flared incisor roots. Braz. Dent. J. 22, 230–237. Silva, N.R., Raposo, L.H., Versluis, A., Fernandes-Neto, A.J., Soares, C.J., 2010. The effect of post, core, crown type, and ferrule
77
presence on the biomechanical behavior of endodontically treated bovine anterior teeth. J. Prosthet. Dent. 104, 306–317. Soares, J.C., Santana, F.R., Castro, C.G., Santos-Filho, P.C.F., Soares, V., Qianb, F., Armstrong, S.R., 2008. Finite element analysis and bond strength of a glass post to intraradicular dentin: comparison between microtensile and push-out tests. Dent. Mater. 24, 1405–1411. Spazzin, A.O., Galafassi, D., de Meira-Ju´nior, A.D., Braz, R., Garbin, C.A., 2009. Influence of post and resin cement on stress distribution of maxillary central incisors restored with direct resin composite. Oper. Dent. 34, 223–229. Valandro, L.F., Zardin, L.W., Villa, M.A., Amaral, M., Galhano, G., Baldissara, P., Bottino, M.A., 2009. Fatigue resistance of teeth restored with fiber posts and different post cementation strengths. Gen. Dent. 57, 264–269. Versluis, A., Messer, H.H., Pintado, M.R., 2006. Changes in compaction stress distributions in roots resulting from canal preparation. Int. Endod. J. 39, 931–939. Wiskott, H.W., Nicholls, J.I., Belser, U.C., 1995. Stress fatigue: basic principles and prosthodontic implications. Int. J. Prosthodont. 8, 105–116.
Available online at www.sciencedirect.com
www.elsevier.com/locate/jmbbm
Research Paper
Fatigue surviving, fracture resistance, shear stress and finite element analysis of glass fiber posts with different diameters Vinı´cius Felipe Wandschera, Ce´sar Dalmolin Bergolib, Ariele Freitas de Oliveirac, Osvaldo Bazzan Kaizera, Alexandre Luiz Souto Borgesd, Ina´cio da Fontoura Limberguere, Luiz Felipe Valandroa,n a
Graduate Program in Oral Science (Prosthodontic Unit), Faculty of Odontology, Federal University of Santa Maria, Santa Maria, Brazil b Division of Prosthodontics, Department of Restorative Dentistry, Federal University of Pelotas, Rio Grande do Sul, Brazil c Faculty of Odontology, Federal University of Santa Maria, Santa Maria, Brazil d Institute of Science and Technology, Univ Est Paulista Julio de Mesquita Filho, São José dos Campos, SP, Brazil e Faculty of Mechanical Engineering, Federal University of Santa Maria, Santa Maria, Brazil
art i cle i nfo
ab st rac t
Article history:
This study evaluated the shear stress presented in glass fiber posts with parallel fiber (01)
Received 26 September 2014
and different coronal diameters under fatigue, fracture resistance and FEA. 160 glass-fiber
Received in revised form
posts (N¼ 160) with eight different coronal diameters were used (DT ¼double tapered,
14 November 2014
number of the post¼ coronal diameter and W¼Wider - fiber post with coronal diameter
Accepted 17 November 2014
wider than the conventional): DT1.4; DT1.8 W; DT1.6; DT2W; DT1.8; DT2.2 W; DT2; DT2.2.
Available online 11 December 2014
Eighty posts were submitted to mechanical cycling (3 106 cycles; inclination: 451; load:
Keywords:
50 N; frequency: 4 Hz; temperature: 37 1C) to assess the surviving under intermittent
Fiber post
loading and other eighty posts were submitted to fracture resistance testing (resistance
Fracture strength
[N] and shear-stress [MPa] values were obtained). The eight posts types were 3D modeled
Mechanical cycling
(Rhinoceros 4.0) and the shear-stress (MPa) evaluated using FEA (Ansys 13.0). One-way
Finite element analysis
ANOVA showed statistically differences to fracture resistance (DT2.2 W and DT2.2 showed
Fractographic analysis
higher values) and shear stress values (DT1.4 showed lower values). Only the DT1.4 fiber posts failed after mechanical cycling. FEA showed similar values of shear stress between the groups and these values were similar to those obtained by shear stress testing. The failure analysis showed that 95% of specimens failed by shear. Posts with parallel fiber (01) may suffer fractures when an oblique shear load is applied on the structure; except the thinner group, greater coronal diameters promoted the same shear stresses. & 2014 Elsevier Ltd. All rights reserved.
n
Corresponding author. Tel.: þ55 55 3220 9276; fax: þ55 55 3220 9272. E-mail addresses: [email protected] (V.F. Wandscher), [email protected] (C.D. Bergoli), [email protected] (A.F. de Oliveira), [email protected] (O.B. Kaizer), [email protected] (A.L. Souto Borges), [email protected] (I.d.F. Limberguer), [email protected] (L.F. Valandro). http://dx.doi.org/10.1016/j.jmbbm.2014.11.016 1751-6161/& 2014 Elsevier Ltd. All rights reserved.
70
1.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Introduction
Researchers have recently studied alternatives for improving the resistance of endodonticaly treated teeth. The amount of remaining coronal structure is used to determine if the use of fiber reinforced posts is necessary to retain the restoration material (Ferrari and Scotti, 2002). Teeth restored with prefabricated metallic posts or cast posts and cores have shown high values of fracture resistance (Silva et al., 2010; Silva et al., 2011). However, the mode of failure for these teeth is unfavorable, causing irreversible fractures and loss of the teeth. This mode of failure can be explained due the elastic modulus of these posts; with metallic posts presenting greater elastic moduli than fiber posts and generating elevated stress concentration on the remaining root structure (Silva et al., 2011; Akkayan and Gülmez, 2002; Ferrari et al., 2000, 2007; Giovani et al., 2009; Hayashi et al., 2006; Li et al., 2011; Padmanabhan, 2010). The elastic modulus is representative of the flexibility of a material, where higher values indicate a hard material and lower values indicating a flexible material (Plotino et al., 2007). The diameter, the type of fiber and the resin material can influence the elastic limit of a pre-fabricated fiber reinforced post (Asmussen et al., 1999). The elastic modulus is related to the stress transmitted to the root, being one of the most important factors in the fracture mechanism (Coelho et al., 2009; Spazzin et al., 2009; Pegoretti et al., 2002). In vitro (Akkayan and Gülmez, 2002; Coelho et al., 2009; Spazzin et al., 2009; Pegoretti et al., 2002) and clinical studies (Ferrari et al., 2000; Ferrari et al., 2007; Schmitter et al., 2007) have shown better or at least comparable performance for fiber reinforced composite posts when compared with cast post and cores and pre-fabricated metallic posts (reparable failures for fiber post approach, while irreparable fractures occur for metal post). Thus, adhesively cemented fiber posts have been indicated as a better option to restore endodonticaly treated teeth, especially in terms of minimal intervention and reducing the risk of root fracture (Ferrari and Scotti, 2002; Ferrari et al., 2000; Ferrari et al., 2007; Malferrari et al., 2003; Monticelli et al., 2003). Static tests are important for assessing the maximum load required for rupture of a specimen. Most articles use the fracture resistance test (loaded at 451) to assess the behavior of fiber posts (Silva et al., 2010, 2011; Akkayan and Gülmez, 2002; Asmussen et al., 1999). However, parallel fiber (01) reinforced polymers usually fracture due to shear stress when submitted at oblique forces. Glass fiber posts are classified as a fiber reinforced polymeric material; where fiber arrangement is crucial in understanding their failure mode. The fiber posts usually present longitudinally organized fibers (parallel 01), which can support high tensile stresses. On the other hand, the shear stresses destructively affect the polymer, indicating that the polymer matrix is important in the calculation of these fracture values (Shipley and Becker, 2002). FEA is a numerical method that help to investigate stress and strain state and combined with experimental test allows obtaining a better understanding of failures, predicting where failure can occur. Hence, the use of both tests is important to obtain a better understanding regarding the mechanical
behavior of a specimen during an event (Farah et al., 1973; Soares et al., 2008; Versluis et al., 2006). Although there are studies showing that fiber reinforced post have good properties, there are some concerns regarding their use to restore weakened roots. Therefore, some techniques have been developed to guarantee better results when restoring weakened roots (anatomic post, accessory fiber post, glass fiber strips, composite resin) (Bonfante et al., 2007; Martelli et al., 2008; Gonçalves et al., 2006; Grandini et al., 2003; Island and White, 2005; Marchi et al., 2003; Miller, 1993). These techniques lead to decreasing the amount of resin cement around the fiber post and provide good fracture resistance to the weakened root. However, these techniques are not easy to perform and require more clinical time when compared to the use of conventional fiber post cementation. Some tapered fiber posts present enlarged coronal/cervical diameters for restoring weakened roots by not requiring excess removal of the intracanal dental structure. Thus, these posts maintain a conservative dimension of the apical portion of a root canal and decrease the resin cement thickness around the post at the weakened portion of the root. These wider posts have a greater taper when compared with conventional posts; however, these posts keep the same fiber/matrix (80/20) ratio. However, there are no studies regarding the fracture resistance or the behavior of this type of post system during mechanical loading. Consequently, this current study aimed to evaluate the fracture resistance, shear stress (in vitro and FEA test) and surviving after intermittent fatigue loading of fiber posts with different coronal wider diameters. The following conceptual hypotheses were tested: (1) fiber posts with increased coronal diameters would present higher rates of fracture resistance; (2) the finite element analysis would show similiar distribution for all groups without difference between real and virtual shear values calculated; (3) fiber posts with increased coronal diameters would present the best behavior during mechanical cycling.
2.
Material and methods
2.1.
Specimen preparation and embedding procedures
The posts used in the study are part of a system of fiberreinforced polymers with double tapered (DT) shape. In this set of posts there are special retainers for larger root canals in which the coronary diameters are wider, but the apical is smaller relative to the other. So the groups was named according to factors: DT (double-tapered)þcoronal diameter (for the wider posts the W letter was added in the name). One hundred sixty fiber posts (White Post DC and White Post DCE systems, FGM, Joinvile, SC, Brazil) (N¼ 160) were allocated into eight groups (n¼20) (Fig. 1A). Each post was attached to a device, keeping its long axis perpendicular to the ground, and embedded with epoxy resin (Sikadur 55 SLV, Osasco, SP, Brazil) in plastic cylinders (height: 15 mm, Ø: 25 mm). The fiber posts from the conventional system (White Post DC) were embedded to a depth of 14 mm, while the wider fiber posts of the special system (White Post DCE) were embedded to a depth of 12 mm. This difference in embedding length was
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
71
Fig. 1 – A. Representative image of the study groups utilized (DT¼ Double tapered and the number, for example, 1.4, indicate the coronal diameter). White letters indicates the group's code, the red upper numbers indicates the coronal diameter and the red lower numbers the apical diameters. B. Specimen positioned during mechanical cycling.
Fig. 2 – Mathematical deduction to calculate the shear stress. τ: shear stress, V: applied force (Fy: Fmax * cos451), Q: static – : center of gravity refers to a semi-circle). The area to be calculated should be taken moment of area (A: area under the circle* y by half as demonstrated in Fig. 6 (SHEAR stress graphic), I: inertia moment of circle area, t: thickness of cross-sectional area (post diameter), π: 3.14 and D: post diameter.
necessary to keep the same length of the fiber posts to the coronal portion (cylindrical region, 6 mm), since conventional posts are 20 mm in length and wider special posts are 18 mm in length. So it was possible to ensure full embedding of tapered region and assure that the load be distributed throughout the cylindrical length of the fiber post.
2.2.
Evaluation of surviving after mechanical cycling
Ten specimens of each group were submitted to mechanical cycling, in a mechanical fatigue simulator (Erios ER 1 force of 11000, Erios, São Paulo, SP, Brazil), applying the protocol as followed: angle- 451; load- 50 N; frequency- 4 Hz; temperature- 737 1C. During the cycling, a cylindrical stainless steel piston (Ø: 6 mm) applied a load to the coronal portion of the post to a maximum of 3,000,000 cycles or until fracture (Fig. 2). Specimens were analyzed after every interval of 250,000 cycles.
2.3.
Fracture resistance test
A stainless steel piston with a diameter of 6 mm, attached to a universal testing machine (EMIC DL 2000, São José dos Pinhais, PR, Brazil), applied a force on the coronal portion of the specimens (Fig. 1B), at a cross head speed of 1 mm/min, 451 of inclination until fracture. The value of fracture resistance (N) of each specimen was defined as the highest point observed in the load x dislodgement curve. After the fracture resistance test, the shear stress value (MPa) of each specimen was calculated. To calculate the shear stress of the cross-section circular area of the fiber post, it was necessary to determine the formula from a universal formula for the shear stress (Fig. 2). Then, the calculation was performed according to the following mathematical equation: τ¼
16:Fmax:cos45 3:π:D2
ð1Þ
where, τ¼shear stress; Fmax.cos45¼refers to vector component Fy, responsible for specimen bending (Fig. 3), Fmax¼ maximum
72
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Fig. 3 – A: Specimen positioned during the fracture resistance test and the vectorial force decomposition (original force at 451). B: Parallelogram Law for calculating force vectors (Hibbeler, 2006; Beer and Johnston, 1994), F: Original Force at 451, HIP: hypotenuse, Fy: vectorial component at Y axis, OS: opposite side to the angle, Fx: vectorial component at X axis and AS: adjacent side to the angle. So, HIP¼F, Fy¼OS and Fx¼AS.
value (N) observed at specimen fracture, cos45¼ cosine of the angle 451; D¼diameter of the post at the coronal portion (mm). Values of “stress” were obtained for each specimen and a mean was calculated for each group.
2.4.
Failure analysis
After evaluating the fracture resistance, all specimens were analyzed using a stereomicroscope at 10x (Discovery V-20, Zeiss, Germany) to detect the type of failure. Some specimens were observed with a scanning electron microscope (SEM) (JSM 5400, Jeol Ltd, Tokyo, Japan).
2.5.
Finite element analysis
The specimens corresponding to the conventional fiber post system (White Post DC, FGM) and wider fiber post system (White Post DCE, FGM) were 3D modeled using the software CAD Rhinoceros (version 4.0SR8 McNell, North America, Seattle, WA, USA) in accordance with the dimensions obtained from the manufacturer (Fig. 1). The epoxy resin was modeled in accordance with the plastic cylinder dimensions (15 mm height and 25 mm diameter). After modeling, the geometries were imported in an.STP format to the Ansys software (Ansys 13.0, Houston, TX, USA) for numerical simulation. Tetrahedron elements were used to generate the mesh using 10 nodes, with a size of 0.2mm, totaling approximately 80,000 elements and 120,000 nodes in each model. The interface between the fiber post and epoxy resin was considered bonded, the lateral and inferior surfaces of the epoxy resin were considered fixed (no displacement) and a force at 45o of angulation was applied to the fiber post. The force applied in each model was the same as the fracture resistance mean obtained in each group after fracture resistance test (Table 1), so the force applied to each group were: DT1.4 - 66 N; DT1.8 W - 144 N, DT 1.6–110 N; DT2W – 170 N; DT1.8–132 N; DT2.2 W – 237 N; DT2–169 N; DT2.2 196 N. The shear stress values (MPa)
were analyzed in each group at a point situated 2 mm above the fulcrum region. In bending the shear stress it is maximum and constant in the average central plan (center) of the post in all extension (6mm), differently the tensile and compressive stresses (Shipley and Becker, 2002). Fiber posts were considered orthotropic (Ex ¼ 37 GPa; Ey ¼9.5 GPa; Ez ¼ 9.5 GPa; vxy ¼0.27; vxz ¼ 0.34; vyz ¼ 0.27; Gxy ¼ 3.1; Gxz ¼ 3.5; Gyz ¼ 3.1) and the epoxy resin was considered isotropic (E¼2.2 GPa; v¼ 0.3). Orthotropic materials present Young modulus values in accordance with the axis (x, y, z), while isotropic materials presented just one value of Young modulus. The elastic and poison values used for fiber post were in accordance with the literature (Lanza et al., 2005), while the values of epoxy resin were obtained from the manufacture (Sikadur, Osasco, SP, Brazil). These values were inserted in the software before execute the analysis.
2.6.
Statistical analysis
The mean values of fracture resistance and shear stress were submitted to One-way ANOVA and Tukey test (α¼0.05). The specimens submitted to mechanical cycling were analyzed in accordance with two conditions: fracture and no fracture.
3.
Results
3.1.
Fracture load and stress analysis
All specimens of DT1.4 fractured during mechanical cycling: five specimens failed between 0 and 250,000 cycles; two specimens failed between 250,000 and 500,000 cycles; two specimens failed between 500,000 and 750,000 cycles; and one specimen failed between 750,000 and 1,000,000 cycles. Other groups did not present failures. One way ANOVA showed a statistically significant difference between the groups, in relation to the fracture strength (po0.001) and shear stress values (po0.001). Fiber posts with smaller coronal diameters showed lower fracture resistance values (N) (Table 1) when compared with fiber posts with wider coronal diameters. However, these fiber posts supported almost the same stress values (MPa) during the test. The fiber posts of the DT1.4 group showed statistically significantly lower shear stress values than did the other groups (Table 1). The graphics load (N) X displacement (mm) cans be observed in Fig. 4. The finite element analysis showed that the shear stress (MPa) achieved higher values at the centrum of the fiber posts and minimal values at the peripheral regions (Fig. 5). The values and the distribution of shear stresses were similar in all groups and similar to the values obtained by the shear stress calculation.
3.2.
Failure analysis
The fracture analysis showed that 95% of the specimens presented a crack along the long axis, perpendicular to the applied direction of the load (Fig. 6ABC). Another 5% of specimens the failure standard was practically in cracks with “Y” appearance (Fig. 6D), with two crack starting at the point
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
73
Table 1 – Means and standard deviation to the values of fracture resistance (N) and shear stress (MPa) after Tukey tests (α ¼0.05). Posts
Coronal Ø (mm)
Mean fracture resistance and standard deviation (N)
Mean shear stress (MPa) and standard deviation
DT1.4 DT1.8W DT1.6 DT2W DT1.8 DT2.2W DT2 DT2.2
1.4 1.8 1.6 2.0 1.8 2.2 2.0 2.2
66.679.01A 140.8977.59B 110.83711.76C 172.91713.82D 132.07711.79B 217.35718.73E 169.27724.66D 196.76712.06E
40.4275.47a 51.7072.78b 51.4875.46b 51.3974.10b 48.4774.32b 53.3974.60b 50.3177.33b 48.3472.96b
* Same letters mean similar statistical results.
Fig. 4 – Representatives images of load (N) X Displacement (mm) graphics of eight groups submitted at fracture resistance. CP: each curve in each graph represents a specimen. of load application that join the center of the specimen ending at the external portion of the post. The fracture analysis with the Scanning Electron Microscope (SEM) presented a characteristic fracture pattern of shear stresses, a crack in the central portion along the long axis of the posts (Fig. 6ABC) in the same sense of the fibers of the posts (parallel fibers).
4.
Discussion
In accordance with Asmussen et al. Asmussen et al. (1999), the highest value of resistance of a post could be obtained using the force X deformation plot. This property is related to the force necessary to cause a fracture or plastic deformation in a material (Anusavice, 2003), leading to catastrophic failure of a specimen (Fig. 4). The results of this current study showed that the fracture resistance values increase as the diameter of the fiber post increases (Table 1), corroborating with the results of Asmussen et al. Asmussen et al. (1999) and confirming the first hypothesis of the study. This result is explained by the fiber posts with smaller diameters (DT1.4) fractured with lower values comparing to another groups with wider diameters Asmussen et al. (1999). A fiber post is composed of longitudinal fibers embedded in an epoxy resin matrix, which is prone to failure due to shear stresses. The parallel configuration of fibers (01) in fiber
posts is very resistant to tensile forces applied along the long axis of the posts. However, when a force is obliquely applied, this resistance can be affected because other types of stresses start acting on this polymer (such as shear stress). Hence, the integrity of the material is impaired, since these posts were not designed to withstand oblique loads. Fracture occurs more easily by shear stress, and occurs at lower numerical values than the tensile stresses that the material supports. Thus, it is also important to perform failure analysis and calculate the shear stress to evaluate this kind of post. Based on the shear stress results, the second hypothesis was partially accepted, since the shear stress obtained by the fiber post DT1.4 was statistically lower than the other groups (Table 1). Normally, the shear stress should be identical for all groups, because the posts are made with the same material and proportions (80% glass fibers and 20% epoxy resin matrix). However, the DT1.4 fiber posts present the smallest coronal diameter (ؼ1.4 mm), which is directly proportional to the shear stress values and generates results that are statistically inferior. In addition, this result corroborates with the failures observed by this type of fiber post after mechanical cycling (all specimens failed), indicating that the DT1.4 fiber post system (Øc¼ 1.4 mm and Øa¼ 0.65 mm) is the most susceptible to shear stress forces than the other groups. The finite element analysis showed a similar distribution of shear stress between the groups, accepting partially the second hypothesis of the study. Additionally, the values of
74
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Fig. 5 – Representatives images of the finite element analysis of each model. In each group was chosen a point for measuring the stress (2 mm above the fulcrum). It is important to observe that the maximum shear stress occur in the central portion of the posts (points A2, B2, C2, D2, E2, F2, G2 and H2) and the minimum shear stress occur in the external portion of the posts. The maximum shear stress values are similar to those obtained by the shear stress calculation (Table 1).
Fig. 6 – Representative image of failure analysis in stereomicroscope (X10). In A, B and C are represent the failures of the 95% of specimens. A and C lateral views and B top view. The red arrow indicates the point of load application and the manual indicator show the cracks. It notes a crack in the long axis and approximately in center of specimen consequence of the shear stress produced during fracture load. In D is the different failure pattern (another 5% of specimens).
Fig. 7 – Representatives micrographics of central portion of posts. To analyze these surfaces has required a cut in the area of the fulcrum. After this cut the portions were detached and observed in SEM. The letters a indicate the fibers, b the matrix, c show the hackles areas (concavities) and d indicate the scallops. As c as d affect the resin matrix. The red arrows indicate the loading direction. Perceives in both A and B, zones shear rupture characteristics, presenting hackles and scallops (“undulations”) in resin portion (matrix) of posts.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
shear stress observed by the finite element analysis (Fig. 5) were similar to those obtained by the formula calculation (Table 1), in all groups. These results prove that the shear stresses are harmful to fiber posts, validating these results and confirming the mechanical behavior of this kind of post. The failure analysis indicated that fiber posts fail by shear stress, since 95% of the specimens showed typical shear stress failure patterns (Figs. 6 and 7). Another 5% of failures present a pattern as in image 5D breaking by shear stress too. This pattern can be explained by small misalignment of the specimen during the embedding. How the test is performed in small areas, a small error in aligning the specimen may to generate this failure pattern, but that does not affect the stress and fracture values. In order to understand the failures, it is necessary to understand the 451 loading on the specimens. As indicated by the parallelogram law, a 451 force must be decomposed into a cartesian axis (Hibbeler, 2006). The combined vector components of X and Y give rise to the original force F at 451 (Fig. 3). The component X causes compressive stresses to the structure (Fig. 8A) while the Y component leads to bending of the post and the appearance of tensile, compression (Fig. 8B) and shear stresses (Fig. 8C). The tensile and compression stresses are maximum in the external portions and minimum at the center (neutral line) (Fig. 8B). The opposite occurred with the shear stress, where the maximum force occurred in the center and minimum forces were at the external surfaces of the posts (Fig. 8C) (Beer and Johnston, 1994). As the shear stress is greatest at the center of the specimen, the fracture tends to occur in this zone, inducing fracture of the structure as presented in Fig. 6. Thus, during bending, the limit of shear resistance is reached before the limit of tensile resistance is attained, because the fiber posts were not designed to support shear stress. The finite element analysis (Fig. 5) and the failure mode evaluation (Fig. 6) support these findings. Fractures in composites can occur in a number of complex ways, due to their laminated orthotropic construction
Fig. 8 – ABC. Representation of the Fx and Fy effects on the structure. C (graphic B): compression, T: tensile, NL: neutral line, σx: normal tension in X axis, A: area, M: static moment of area, C (formula): distance from neutral line to the more requested fiber, I: inertia moment of the area,τ: shear stress, V: applied force (Fy¼ Fmax * cos451), Q: static moment of area (A: circular area) and t: thickness of cross-sectional area (post diameter).
75
(the fracture depends on the direction of applied load and the orientation of fibers). Fractures in continuous fiber reinforced composites can be divided into three basic fracture types: interlaminar (fractures oriented between plies), intralaminar (fractures located internally within a ply) and translaminar (involving significant fiber fractures). For these cases, interlaminar and intralaminar fractures occur on a plane that is parallel to that of fiber reinforcement. The interlaminar and intralaminar fractures occur under mode I tension (generated under interlaminar tension), mode II in-plane shear (separation under shear loading occurs by coalescence of numerous tensile microcracks under continued shear displacement) and mode III anti-plane shear (which have not been thoroughly studied) (Shipley and Becker, 2002). As inter- and intralaminar fractures occur in the same plane as their fiber reinforcement, their fracture mechanism and appearance tend to be dominated by fracture of the matrix and fiber-to-matrix separation. In addition, Fig. 7 presents a distinct branched structure that exists on both sides of the hackles and scallops, where they intersect adjoining areas of fiber-to-matrix separation (Shipley and Becker, 2002). These failures are classified as intralaminar mode II in-plane shear. Several fiber posts (fiber-reinforced polymer) are commercially available. Most of them, such fibers are arranged in parallel along the post. Thus, in situations where an anterior tooth (451 of inclination) should be restored, it is very important to understand how these forces act on these teeth, especially on bending (tensile, compression and shear stresses). The arrangement of the fibers plays great importance when a force is applied to this structure. Fiber posts with parallel fibers efficiently support tensile, but in bending these fibers are not as efficient. This leads to the failure by shear. In teeth restored with fiber posts, a core is made with composite resin. This causes an increase in resistance, but it does not prevent the bending movement of the restorative assembly. In addition to the in vitro tests, dynamic tests, such as fatigue, are important for predicting the material behavior. Mechanical cycling has been used for testing the bond between fiber posts and root canals (Bergoli et al., 2011; Bottino et al., 2007; Rosa et al., 2011; Valandro et al., 2009), the behavior of endodontically treated teeth restored with post retainers (Bolhuis et al., 2004; Santini et al., 2011; Reid et al., 2003) and for evaluating the properties of different restorative materials (Rached et al., 2011; Scherrer et al., 2011). Mechanical cycling is an important test because it can generate a catastrophic failure from defects inside the material, after long periods of cycling (Wiskott et al., 1995), which is similar to what occurs clinically. As prospective studies, the researchers should investigate if the findings/ outcomes with fiber posts observed by us will occur when restoring root canals with fiber post, core and crown. Based on the results obtained after mechanical cycling, the third hypothesis of the study was partially accepted, because even though all specimens of group DT1.4 fractured during mechanical cycling, the other groups did not present failures after three million cycles. This outcome could be related to the fact that the fracture resistance mean of fiber post DT1.4 (Øc¼ 1.4 and Øa¼ 0.65) was inferior to the load used during mechanical cycling, allowing the fiber post to
76
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
reach its elastic limit. Also, this study performed 3,000,000 cycles, corresponding to three years of clinical service (Wiskott et al., 1995). It has been proposed that, if more cycles had been applied, the other groups might have failed.
5.
Conclusion
1- Fiber posts with fibers arranged parallel to the long axis presented failures by shear stress forces when loading at 451. 2- The DT1.4 fiber post appears to be less resistant to fracture than the other posts. 3- The fracture resistance of a fiber post increases when increasing the coronal diameter. 4- Finite element analysis, in association with in vitro test, validates the hypothesis that fiber posts failure by shear stress when forces are loading at 451.
Acknowledgments The authors thank CAPES (Brazilian Higher Education Agency, Brazil) and CNPq (National Council for Scientific Development and Technology, Brazil) by supporting this investigation. They also thank FGM (Joinville, SC, Brazil) for material donation.
references
Akkayan, B., Gu¨lmez, T., 2002. Resistance to fracture of endodontically treated teeth restored with different post systems. J. Prosthet. Dent. 87, 431–437. Anusavice, K.J., 2003. Philips’ Science of Dental Materials, eleventh ed. Saunders Co., St. Louis. Asmussen, E., Peutzfeldt, A., Heitmann, T., 1999. Stiffness, elastic limit, and strength of newer types of endodontics posts. J. Dent. 27, 275–278. Beer, F.P., Johnston Jr., R., 1994. Vector Mechanics for Engineers Statics, fifth ed. Makron Books do Brasil. Bergoli, C., Amaral, M., Baldissara, P., Valandro, L.F., 2011. Surviving of bovine teeth adhesively restored with 3 types of fiber post after fatigue resistance. Minerva Stomatol. 60, 303–309. Bolhuis, P., Gee, A., Feilzer, A., 2004. Influence of fatigue loading on four post-and-core systems in maxillary premolars. Quintessence Int. 35, 657–667. Bonfante, G., Kaizer, O.B., Pegoraro, L.F., do Valle, A.L., 2007. Fracture strength of teeth with flared root canals restored with glass fibre posts. Int. Dent. J. 57, 153–160. Bottino, M.A., Baldissara, P., Valandro, L.F., Galhano, G.A., Scotti, R., 2007. Effects of mechanical cycling on the bonding of zirconia and fiber posts to human root dentin. J. Adhes. Dent. 9, 327–331. Coelho, C.S., Biffi, J.C., Silva, G.R., Abraha˜o, A., Campos, R.E., Soares, C.J., 2009. Finite element analysis of weakened roots restored with composite resin and posts. Dent. Mater. J. 28, 671–678. Farah, J.W., Craig, R.G., Sikarskie, D.L., 1973. Photoelastic and finite element stress analysis of a restored axisymmetric first molar. J. Biomech. 6, 511–520. Ferrari, M., Scotti, R., 2002. Fiber Posts. Theoretical Considerations and Clinical Applications, first ed. Milan, Masson39–41.
Ferrari, M., Vichi, A., Garcı´a-Godoy, F., 2000. Clinical evaluation of fiber-reinforced epoxy resin posts and cast post and cores. Am. J. Dent. 13, 15B–18B. Ferrari, M., Cagidiaco, M.C., Goracci, C., Vichi, A., Mason, P.N., Radovic, I., Tay, F., 2007. Long-term retrospective study of the clinical performance of fiber posts. Am. J. Dent. 20, 287–291. Giovani, A.R., Vansan, L.P., Sousa Neto, M.D., Paulino, S.M., 2009. In vitro fracture resistance of glass-fiber and cast metal posts with different lengths. J. Prosthet. Dent. 101, 183–188. Gonc¸alves, L.A., Vansan, L.P., Paulino, S.M., Sousa Neto, M.D., 2006. Fracture resistance of weakened roots restored with a transilluminating post and adhesive restorative materials. J. Prosthet. Dent. 96, 339–344. Grandini, S., Sapio, S., Simonetti, M., 2003. Use of anatomic post and core for reconstructing an endodontically treated tooth: a case report. J. Adhes. Dent. 5, 243–247. Hayashi, M., Takahashi, Y., Imazato, S., Ebisu, S., 2006. Fracture resistance of pulpless teeth restored with post-cores and crowns. Dent. Mater. 22, 477–485. Hibbeler, R.C., 2006. Mechanics of Materials, fifth ed. Prentice Hall, Sa˜o Paulo Pearson. Island, G., White, G.E., 2005. Polyethylene ribbon fibers: a new alternative for restoring badly destroyed primary incisors. J. Clin. Pediatr. Dent. 29, 151–156. Lanza, A., Aversa, R., Rengo, S., Apicella, D., Apicella, A., 2005. 3D FEA of cemented steel, glass and carbon posts in a maxillary incisor. Dent. Mater. 21, 709–715. Li, Q., Yan, P., Chen, Z., 2011. Fracture resistance and failure patterns of open apex root teeth with different posts after endodontic treatment. J. Huazhong. Univ. Sci. Technol. Med. Sci. 31, 271–276. Malferrari, S., Monaco, C., Scotti, R., 2003. Clinical evaluation of teeth restored with quartz fiber-reinforced epoxy resin posts. Int. J. Prosthodont. 16, 39–44. Marchi, G.M., Paulillo, L.A., Pimenta, L.A., Lima, F.A., 2003. Effect of different filling materials in combination with intraradicular posts on the resistance to fracture of weakened roots. J. Oral. Rehab. 30, 623–629. Martelli Jr., H., Pellizzer, E.P., Rosa, B.T., Lopes, M.B., Gonini Jr., A., 2008. Fracture resistance of structurally compromised root filled bovine teeth restored with accessory glass fibre posts. Int. Endod. J. 41, 685–692. Miller, T.E., 1993. A new material for periodontal splitting and orthodontic retention. Comp. Cont. Educ. Dent. 14, 802–804. Monticelli, F., Grandini, S., Goracci, C., Ferrari, M., 2003. Clinical behavior of translucent-fiber posts: a 2-year prospective study. Int. J. Prosthodont. 16, 593–596. Padmanabhan, P., 2010. A comparative evaluation of the fracture resistance of three different pre-fabricated posts in endodontically treated teeth: an in vitro study. J. Conserv. Dent. 13, 124–128. Pegoretti, A., Fambri, L., Zappini, G., Bianchetti, M., 2002. Finite element analysis of a glass fibre reinforced composite endodontic post. Biomaterials 23, 2667–2682. Plotino, G., Grande, N.M., Bedini, R., Pameijer, C.H., Somma, F., 2007. Flexural properties of endodontic posts and human root dentin. Dent. Mater. 23, 1129–1135. Rached, R.N., Souza, E.M., Dyer, S.R., Ferracane, J.L., 2011. Dynamic and static strength of an implant-supported overdenture model reinforced with metal and nonmetal strengtheners. J. Prosthet. Dent. 106, 297–304. Reid, L.C., Kazemi, R.B., Meiers, J.C., 2003. Effect of fatigue testing on core integrity and post microleakage of teeth restored with different post systems. J. Endod. 29, 125–131. Rosa, R.A., Bergoli, C.D., Kaizer, O.B., Valandro, L.F., 2011. Influence of cement thickness and mechanical cycling on the push-out bond strength between posts and root dentin. Gen. Dent. 59, 156–161.
journal of the mechanical behavior of biomedical materials 43 (2015) 69 –77
Santini, M.F., Wandscher, V., Amaral, M., Baldissara, P., Valandro, L.F., 2011. Mechanical fatigue cycling on teeth restored with fiber posts: impact of coronal grooves and diameter of glass fiber post on fracture resistance. Minerva Stomatol. 60, 485–493. Scherrer, S.S., Cattani-Lorente, M., Vittecoq, E., de Mestral, F., Griggs, J.A., Wiskott, H.W., 2011. Fatigue behavior in water of Y-TZP zirconia ceramics after abrasion with 30 μm silicacoated alumina particles. Dent. Mater. 27, 28–42. Schmitter, M., Rammelsberg, P., Gabbert, O., Ohlmann, B., 2007. Influence of clinical baseline findings on the survival of 2 post systems: a randomized clinical trial. Int. J. Prosthodont. 20, 173–178. Shipley, R.J., Becker, W.T., 2002. Failure analysis continuous fiber reinforced composites. In: tenth ed. In: Smith, T.W., Grove, R.A. (Eds.), ASM Handbook: Failure Analysis and Prevention, volume 11. ASM International, Ohio, pp. 731–743. Silva, G.R., Santos-Filho, P.C., Simamoto-Ju´nior, P.C., Martins, L.R., Mota, A.S., Soares, C.J., 2011. Effect of post type and restorative techniques on the strain and fracture resistance of flared incisor roots. Braz. Dent. J. 22, 230–237. Silva, N.R., Raposo, L.H., Versluis, A., Fernandes-Neto, A.J., Soares, C.J., 2010. The effect of post, core, crown type, and ferrule
77
presence on the biomechanical behavior of endodontically treated bovine anterior teeth. J. Prosthet. Dent. 104, 306–317. Soares, J.C., Santana, F.R., Castro, C.G., Santos-Filho, P.C.F., Soares, V., Qianb, F., Armstrong, S.R., 2008. Finite element analysis and bond strength of a glass post to intraradicular dentin: comparison between microtensile and push-out tests. Dent. Mater. 24, 1405–1411. Spazzin, A.O., Galafassi, D., de Meira-Ju´nior, A.D., Braz, R., Garbin, C.A., 2009. Influence of post and resin cement on stress distribution of maxillary central incisors restored with direct resin composite. Oper. Dent. 34, 223–229. Valandro, L.F., Zardin, L.W., Villa, M.A., Amaral, M., Galhano, G., Baldissara, P., Bottino, M.A., 2009. Fatigue resistance of teeth restored with fiber posts and different post cementation strengths. Gen. Dent. 57, 264–269. Versluis, A., Messer, H.H., Pintado, M.R., 2006. Changes in compaction stress distributions in roots resulting from canal preparation. Int. Endod. J. 39, 931–939. Wiskott, H.W., Nicholls, J.I., Belser, U.C., 1995. Stress fatigue: basic principles and prosthodontic implications. Int. J. Prosthodont. 8, 105–116.
